The smuggling was not minor and the statements are not in contradiction to each other; Southern authorities allowed the trade at that time for the very obvious reason they needed supplies and gold to fund the war effort. Sending Cotton to the North in exchange for repeaters in the South in 1862 is a deal Richmond would see as necessary but allowing unsanctioned peace time trade that undermines both Confederate foreign policy as well as the economy is not. The strategic situation from 1862 to, say, 1868 would thus be very different resulting in different policies.GU
So actually the smuggling you mentioned earlier was minor in impact. As I said however this would be more of a problem for the south than the north. [Especially if due to corruption it might end up as less than minor].
The statement could be read that way as well true.
Some strongmen may have occasionally displayed what could be said as interest in leaving Mexico. IIRC the person you mentioned before reversed their position within a short period of time. However the viewpoint of the bulk of the population, especially with the poor treatment of the Mexicans in the US and the threat seen by slavery, is probably likely to be less friendly.
You mentioned one comment by a pro-southern former governor but comnents in papers often relate more to personal desires and beliefs rather than actual hard facts. For instance a bit further down it mentions. Also that link also mentions that while divided on the issue of the secession of the other states New Jersey fully supported the war.
Also a bit above this of the large crowds that welcomed Lincoln even before this. Similarly the presence of a large pro-abolition movement in the state and of a sizeable number of blacks, either freed under the states emancipation policy passed in 1804 or who had settled there having escaped from the south.
With regards to Vidaurri, he never changed his position and in fact it was Jefferson Davis who declined the offer. The reasoning behind this was because Davis wished to keep Vidaurri's ports open for Confederate trade with Europe, since the Union could not legally blockade them and this enabled the importation of goods from Europe and elsewhere unmolested; if Vidaurri joined the Confederacy in 1861, this would clearly change and enable the Union Navy to cut off this trade. Here again, we see what I was just talking about in terms of individuals responding to the situations at hand. With regards to the issue of Slavery, as already shown by quoting Noel Maurer, this was not an issue in Northern Mexico.
With regards to the issue of New Jersey and the economic blow of a successful Confederacy, support for the war is not a good metric nor is free blacks or an abolitionist movement. As already shown, an illicit trade in cotton was carried out and the war-time economy created artificial conditions that, once demobilization came, would cease to exist. As the former Governor noted, most of New Jersey's production went to the South and said South, in the event of a C.S. victory, would be behind a new tariff wall making European or domestically produced Confederate goods better options to Southern consumers. Whether or not many New Jersey men served in the Union Army doesn't invalidate the very simple calculus that Southerners not buying their goods would damage their economy in the long run; indeed, that could be the reason New Jersey supplied so many men in the first place, to prevent such from happening.